To quantify these statements, we may write down the diffusive damping time as ? D = 1 / k ?" 2 D, where k ?" is the wave number perpendicular to the magnetic field.
42.
When the wave propagates in inhomogeneous seismic media the propagation constant k must be a complex value that includes not only an imaginary part, the frequency-dependent attenuation coefficient, but also a real part, the dispersive wave number.
43.
Where ? is the growth rate, k is the wave number, a is the radius of the bubble cylinder, T is the surface tension, ? is the circulation, and K 0 and K 1 are Bessel functions.
44.
Whether a component decays or grows, and how fast it grows is entirely a function of its wave number ( a measure of how many peaks and troughs per centimeter ) and the radius of the original cylindrical stream.
45.
The filter width \ Delta has an associated cutoff wave number k _ { c }, and the temporal filter width \ tau _ { c } also has an associated cutoff frequency \ omega _ { c }.
46.
Whether a component decays or grows, and how fast it grows is entirely a function of its wave number ( a measure of how many peaks and troughs per centimeter ) and the radii of the original cylindrical stream.
47.
The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number 0 } } or a " Turing bifurcation " to a globally patterned state with a dominant finite wave number.
48.
The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number 0 } } or a " Turing bifurcation " to a globally patterned state with a dominant finite wave number.
49.
Where a is the scattering length, k is the wave number, and \ delta ( k ) is the s-wave phase shift . The elastic cross section, \ sigma _ e, at low energies is determined solely by the scattering length,
50.
In the standard scattering problem, the incoming beam is assumed to take the form of a plane wave of wave number, which can be decomposed into partial waves using the plane wave expansion in terms of spherical Bessel functions and Legendre polynomials:
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